Need help with NLopt AUGLAG termination criteria

I have an optimization problem with equality constraints and I use NLopt LN_AUGLAG solver with derivative-free local solver like LN_NELDERMEAD or LN_SBPLX. However I don’t have a clear understanding how to choose tolerance for both local and LN_AUGLAG solvers. Is there any intuition how they should correlate?
Ex, I want to find min_x of an objective function f(x) with constraintsg(x)=0. And I know that there is a single solution to this problem.

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